Stl Files and Adding Bases
How to add a flat base:

First of all, you need to reposition your mesh so that it is horizontal. After that, select your mesh, press Shift + D, click (don't move the mouse), and drag the new mesh down along the Z-axis. Now go into Edit mode, with Tab, select everything with A, press S to scale, Z (limit scaling to Z-axis) and 0. Your mesh should be flat. Go into Object mode, select both your objects, press Ctrl + J to join objects, go into Edit mode again, select the outer edges of both surfaces with Alt + RMB, press Ctrl + E, select Bridge edge loops, and you're basically done.
The result should look a bit like this: